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Date	November 2020	Marks available	1	Reference code	20N.1.SL.TZ0.T_6
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 0
Command term	Find	Question number	T_6	Adapted from	N/A

Question

Srinivasa places the nine labelled balls shown below into a box.

Srinivasa then chooses two balls at random, one at a time, from the box. The first ball is not replaced before he chooses the second.

Find the probability that the first ball chosen is labelled $A$ $A$ .

[1]

a.i.

Find the probability that the first ball chosen is labelled $A$ $A$ or labelled $N$ $N$ .

[1]

a.ii.

Find the probability that the second ball chosen is labelled $A$ $A$ , given that the first ball chosen was labelled $N$ $N$ .

[2]

Find the probability that both balls chosen are labelled $N$ $N$ .

[2]

Markscheme

$\frac{3}{9} (\frac{1}{3}, 0.333, 0.333333 \dots, 33.3 %)$ $\frac{3}{9} (\frac{1}{3}, 0.333, 0.333333 \dots, 33.3 %)$ (A1) (C1)

[1 mark]

a.i.

$\frac{5}{9} (0.556, 0.555555 \dots, 55.6 %)$ $\frac{5}{9} (0.556, 0.555555 \dots, 55.6 %)$ (A1) (C1)

[1 mark]

a.ii.

$\frac{3}{8} (0.375, 37.5 %)$ $\frac{3}{8} (0.375, 37.5 %)$ (A1)(A1) (C2)

Note: Award (A1) for correct numerator, (A1) for correct denominator.

[2 marks]

$\frac{2}{9} \times \frac{1}{8}$ $\frac{2}{9} \times \frac{1}{8}$ (M1)

Note: Award (M1) for a correct compound probability calculation seen.

$\frac{2}{72} (\frac{1}{36}, 0.0278, 0.0277777 \dots, 2.78 %)$ $\frac{2}{72} (\frac{1}{36}, 0.0278, 0.0277777 \dots, 2.78 %)$ (A1) (C2)

[2 marks]

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

Syllabus sections

Topic 4—Statistics and probability » SL 4.5—Probability concepts, expected numbers

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Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams

Topic 4—Statistics and probability

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